Spatial Service Systems Modelled as Stochastic Integrals of Marked Point Processes

Poisson processes;Marked point processes;Thinning

Jones, Matthew O. ; Industrial and Systems Engineering

University:Georgia Institute of Technology

Department:Industrial and Systems Engineering

关键词: Poisson processes;    Marked point processes;    Thinning;   

Others  :  https://smartech.gatech.edu/bitstream/1853/7174/1/jones_matthew_o_200508_phd.pdf

美国|英语

来源: SMARTech Repository

【 摘 要 】

We characterize the equilibrium behavior of a class of stochastic particle systems, whereparticles (representing customers, jobs, animals, molecules, etc.) enter a space randomly through time, interact, and eventually leave. The results are useful for analyzing the dynamics of randomly evolving systems including spatial service systems, species populations, and chemical reactions. Such models with interactions arise in the study of species competitions and systems where customers compete for service (such as wireless networks).The models we develop are space-time measure-valued Markov processes. Specifically, particles enter a space according to a space-time Poisson process and are assigned independent and identically distributed attributes. The attributes may determine their movement in the space, and whenever a new particle arrives, it randomly deletes particles from the system according totheir attributes.Our main result establishes that spatial Poisson processes are natural temporal limits for a large class of particle systems. Other results include the probability distributions of the sojourn times of particles in the systems, and probabilities of numbers of customers in spatial polling systemswithout Poisson limits.